Design guide IDP2303(A)
LLC design
Application Note
27
Revision 2.0
2017-05-03
4.2.2.3
Calculation of transformer turn ratio
In the above section, the actual minimum frequency
𝑓
𝑚𝑖𝑛
has been calculated as 87 kHz.
Figure 20
Flux density swing
According to the flux density swing illustrated in Figure 20, the voltage across the primary winding can be
calculated as
𝑉
𝑝
= 𝑛
𝑒
(𝑉
𝑜
+ 𝑉
𝑓
).
The half switching cycle period is around
𝑡 =
1
2𝑓
. According to Faraday’s law:
𝑛
𝑒
(𝑉
𝑜
+ 𝑉
𝑓
)
2𝑓
= 𝑁
𝑝
𝐴
𝑒
∆B
The number of turns on the primary side can be found by:
𝑁
𝑃
=
𝑛
𝑒
(𝑉
𝑜
+ 𝑉
𝑓
)
2𝑓 ∗ 𝐴
𝑒
∆𝐵
Where
𝐴
𝑒
= 88 𝑚𝑚
2
with an EFD38 core.
T
B
62
.
0
is selected to avoid magnetic saturation.
Then
𝑁
𝑝𝑚𝑖𝑛
can be calculated at minimum bus voltage
𝑉
𝑏𝑢𝑠_𝑚𝑖𝑛
by:
𝑁
𝑝𝑚𝑖𝑛
=
𝑛
𝑒
(𝑉
𝑜
+ 𝑉
𝑓
)
2𝑓
𝑚𝑖𝑛
∗ 𝐴
𝑒
∆𝐵
=
7.5 ∗ (24 + 0.5)
2 ∗ 87 ∗ 10
−3
∗ 88 ∗ 10
−6
∗ 0.62
= 20
The selection of the number of turns on the primary side must also take other factors into consideration. For
example, to minimize the circulating current in the primary side due to the magnetizing current, a relatively
larger magnetizing inductance is preferred. Furthermore, the number of turns on the secondary side for 24 V
and 12 V should be integers. The selection is also limited by the structure of the EFD38 transformer available.
Lastly, the number of turns on the primary side is selected as
𝑁
𝑝
= 51
. The secondary side turns for 24 V
and 12 V can then be calculated accordingly by:
𝑁
𝑠_24𝑉
=
𝑁
𝑝
𝑛
= 6
𝑁
𝑠_12𝑉
=
𝑁
𝑠_24𝑉
2
= 3
